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TABLE 4.3
Transfer Matrix for a Beam Element, Part c:
λ>
0,
λ ζη>
0
λ =
0 ,
λ ζη =
1
4
2
1
4
2 ,
1
4
2
λ<
0
λ ζη =
η)
λ ζη<
η)
ζ η =
0
λ ζη>
η)
0
1.
2.
4.
6.
8.
2
2
1
2
b 2
a 2 ,p
A
=
cosh a
, B
=
cos b
ζ>
0:
α
= ζ
ζ η>
0:
β
=
η)
ζ η>
0: g
=
=
1
A
=
cosh a
, B
=
cos b
C
=
sinh a
, D
=
sin b
A
=
cos a
A
=
cos
β
, B
= β
sin
β
A
=
cos a
, B
=
cos b
C
=
sinh a
, D
=
sin b
2 λ ζη
a 2
b 2
g
=
+
B
= (
sin a
)/α
C
= (
sin
β)/β
C
=
sin a
, D
=
sin b
= β
2 η) 4 + η)
1
1
4 η)
a 2
=
a 2
1
4 + η)
1
2 η)
a 2
1
4
+
2
=
2
λ
2 λ ζη +
= β
2 η) + 4 + η)
3.
5.
b 2
1
1
4 η)
=
b 2
1
4 + η)
1
2 η)
b 2
1
4
+
2
+
2
2
1
2 η)
=
2
λ
ζ<
0:
α
=− ζ
ζ η<
0:
β
=−
4
β
=− λ
A
=
cosh
α
A
=
cosh
β
, B
=− β
sinh
β
B
= (
sinh
α)/α
C
= (
sinh
β)/β
7.
ζ η<
a 2
b 2 , p
0: g
=
=−
1
A
=
cosh a
, B
=
cosh b
C
=
sinh a
, D
=
sinh b
η) + 4 + η)
a 2
1
2
=−
2
λ
2 η) 4 + η)
1
b 2
2
=−
λ
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